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Let C= 60o ⇒ B + A = 120o.
Also tan (A – B)/ 2 = (a – b)/(a + b) cot C/2
= (√3 + 1 - √3 + 1) / (√3 + 1 + √3 – 1) cot 30o
= 1
⇒ (A – B)/2 = 45o
⇒ A – B = 90o
⇒ A = 105o, B = 15o
Also c = a sin / sin A = (√3 + 1)/ sin 60° cos 45° + cos 60° sin 45°
= √2(√3 + 1). √3/(√3 + 1) = √6.
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